半线性椭圆能量向量值极小元的比较原理及其对死核的应用
A comparison principle for vector valued minimizers of semilinear elliptic energy, with application to dead cores
摘要：
我们建立了一个比较原理，提供了准确的上界的模向量值极小的能量泛函，相关的潜力是光滑的，椭圆梯度系统。我们的假设非常温和：我们假设势是下连续的，并且在其极小值的邻域内满足单调性条件。作为结果，我们给出了一个充分条件的死核心区域的存在，其中的最小值等于一个最小的潜力。
英文摘要：
We establish a comparison principle providing accurate upper bounds for the modulus of vector valued minimizers of an energy functional, associated when the potential is smooth, to elliptic gradient systems. Our assumptions are very mild: we assume that the potential is lower semicontinuous, and satisfies a monotonicity condition in a neighborhood of its minimum. As a consequence, we give a sufficient condition for the existence of dead core regions, where the minimizer is equal to one of the minima of the potential.
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